Deutsche Bank has hired one of its top shareholders, New York private-equity firm Cerberus Capital Management LP, as a paid adviser to help the troubled lender tackle runaway costs and boost lagging profits.

The appointment of Cerberus comes as Chief Executive Christian Sewing tries to revive the German bank’s fortunes after three consecutive full-year losses, market-share declines and strategic upheaval. Cerberus President Matt Zames, the former chief operating officer of JPMorgan Chase & Co., is leading the advisory...